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If x=3+2root2.Find x+1/x

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If x=3+2root2.Find x+1/x

Posted by Reena Karim 8 years, 4 months ago

CBSE > Class 09 > Mathematics

3 answers

Niranjana Srinivasan 5 years, 3 months ago

x = 3 + 2√2 (Given) 1/x = 1/3 + 2√2 Rationalization of 1/x 1*3 - 2√2 / 3 + 2√2 * 3 - 2√2 = 3 - 2√2 So, now we know that x = 3 + 2√2 1/x = 3 - 2√2 x + 1/x = 3 + 2√2 + 3 - 2√2 = 3 + 3 =6

Arpita Banerjee 8 years, 4 months ago

Given x = 3 + 2√2
⇒ x = 2 + 1 + 2√2
⇒ x = (√2)² + 1² + 2×√2×1
⇒ x = (√2 + 1)²
∴ x = (√2 + 1)
⇒(1/x) = 1/ (√2 + 1)
Multiply and divide by (√2 − 1)
⇒(1/x) = (√2 − 1) / [(√2 + 1)(√2 − 1)]
⇒(1/x) = (√2 − 1) / [2 − 1]
∴ (1/x) = (√2 − 1)
Consider [x + (1/x)] = [(√2 + 1) + (√2 − 1)]
= 2√2

Akash Champ 8 years, 4 months ago

1/x = 1/3+2root2. 1/x= 1/3+2root2 * 3-2root2/3-2root2 1/x = 3-2root 2/3 Sq. -2root2 sq. 1/x = 3- 2root2/9-8 1/x=3-2root2. x+1/x=3+2root2 +3-2root2 x+1/x= 3+3 x+1/x=6. (Answer)

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